Regularization of EIT reconstruction based on multi-scales wavelet transforms

Abstract

Electrical Impedance Tomography (EIT) intends to obtain the conductivity distribution of a domain from the electrical boundary conditions. This is an ill-posed inverse problem usually solved on finite element meshes. Wavelet transforms are widely used for medical image reconstruction. However, because of the irregular form of the finite element meshes, the canonical wavelet transforms is impossible to perform on meshes. In this article, we present a framework that combines multi-scales wavelet transforms and finite element meshes by viewing meshes as undirected graphs and applying spectral graph wavelet transform on the meshes.